Circles are deceptively simple stimuli. When the relative positions of two or more circles are manipulated, different perceived shapes emerge, depending on geometrical constraints that have not been clearly identified so far. Consider relative size and eccentricity of circles as critical variables. While isolated circles are preferentially perceived as flat frontoparallel disks, the composition of two circles, one surrounding the other, elicits the three-dimensional lampshade percept that Michotte, Thinès, and Crabbé (1967) labeled as a typical case of amodal complement “à decouvert” (i.e., without occlusion). The lampshade percept is robust enough to tolerate eccentricities that are incompatible with straight cone geometry, as demonstrated by the fact that observers easily perceive a lampshade with a concave mantle when the eccentricity is increased beyond the limits of inclusion of one circle within the other. Compositions of three or more regularly spaced circles are even more interesting, given that they are perceived as a set of overlapping disks only in the absence of a common axis. When their centers are collinear, circles are perceived as a structure of connected balls: a solution which is consistent with the “eggs” demonstration discussed by Tse (1999). Taken together, such phenomena suggest that the competition between alternative visual shapes is constrained by relatively local principles (unidirectional function of borders, minimal depth), as well as by global principles (view genericity at the level of the overall structure). In the absence of textural, kinetic, and shading information, volume perception can be supported by configural factors alone.